There are some very cool boardgames that have mechanics that would be very interesting to use for RPGs.
First thing is Five Parsecs from Home, which is a miniatures wargame. It has a really amazing enemy intelligence system that lets it be played as a solo game. Lots of wargames/boardgames have solo rules or enemy intelligence, but 5 Parsecs' rules are especially good, adding lots of flavor to how enemies act without adding a lot of work or "crunch". Not only is it great for solo gaming, but I think it works really well as a guide for newbie GMs. I was teaching someone recently how to GM D&D5e, and it was going really smooth until we got to running enemies in combat. They didn't have a wargame background, so all the tactics and strategy stuff is new to them. Now, if they had 5 Parsecs they could use that AI system to run enemies in combat, and that would at the very least give them a baseline that they could use if they want and ignore when they don't.
Firefly Adventures: Brigands & Browncoats is a miniatures boardgame that plays a lot like an RPG. It does "heists" (or whatever kind of clandestine activity) in a really interesting way that really fleshes it out. Pretty much everything it does could be used in an RPG, and it could really make sneaking around more exciting in "traditional" RPGs (stuff like Blades in the Dark doesn't need it). The initiative system is really interesting as well, and it helps make sneaking around tense as you're on a very engaging clock.
Pulp Alley is a miniatures wargame that has some amazingly creative scenarios. It's a wargame, but depending on the scenario, you might not be fighting anyone. Some scenarios are about meeting up with an informant before the enemy finds them. There's some where you are investigating a murder. There's quite a few where you are exploring somewhere, like a ruin or a jungle. It also has really great solo rules (and the thing is, the solo rules from these games have a vastly different feel than the solo RPGs I've seen). It's kind of funny, since it's so much like an RPG, the author decided to make an RPG version, so he asked the community what the game needed in order to be more like an RPG. No one could think of anything as it's basically all there already, so they scrapped the idea.
Battlestations 2e is a miniatures boardgame that is very much like an RPG (so much so I'm not sure where the line is). It has an amazing spaceship battle system, and is better than any RPG spaceship system I have ever seen. It's actually what the videogame FTL: Faster Than Light was based on. It's funny, because even though it never claims to be an RPG, there is a rule in the book where the author says "You will never need this rule if you are playing this as a boardgame." The only time it would possibly be useful is if you had a GM running it like an RPG.
Deadzone is a miniatures wargame/boardgame (there's actually some disagreement on what it qualifies as) and it has the BEST grid/measurement system. Period. So, the game uses 3" by 3" cubes. When you move to a cube, you can position anywhere within that cube. This gives you all the best qualities of grid and non-grid measuring, while actually being faster and easier than either. Which, includes making the use of 3d terrain extremely fun and easy. It's also the game that taught me why 3d terrain is so much fun, which is "true line of sight". TLOS is the most fun and immersive way to check for line of sight and cover, and really makes cool looking terrain feel useful and important. Definitely not as big of a deal for non-shooting games, but I still think it adds a lot.
Frostgrave/Stargrave has an amazing system for what I'm going to call "light PvP". It's mostly designed to be versus, but also has coop and solo modes, but the important thing is that the PvP isn't required, even in a normal game. The objective is to raid the ruins and get the loot, sometimes fighting NPCs and monsters. You want to attack the other PCs? Go for it, but that doesn't mean you are going to "win". You can focus on being defensive, or sneaky, or tricky, and not necessarily worry about how killy your team is, and still have a great time and even "win" (being aggressively killy can work too though). There are also some great campaigns, including some that are pseudo-coop (basically, everyone has to work together if they want to survive).
I could go on and on. Scenario design from Rangers of Shadow Deep, Rogue Stars being basically a great sci-fi RPG (though you have to drop its super cool initiative system), running investigative campaigns using 5150 New Beginnings PI, etc.
